Binary scaling: Difference between revisions

Revision as of 21:42, 6 August 2019

Revision as of 03:00, 8 August 2019

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A position for the 'binary point' is chosen for each variable to be represented, and binary shifts associated with arithmetic operations are adjusted accordingly. The binary scaling corresponds in [[Q (number format)]] to the first digit, i.e. Q1.15 is a 16 bit integer

scaled with one bit as integer and fifteen as fractional. A Bscal 1 or Q1.15 number would represent approx 1.999 to -2−2.0 as [[floating point]].

To give an example, a common way to use [[arbitrary-precision arithmetic|integer arithmetic]] to simulate floating point, using 32 bit numbers, is to multiply the coefficients by 65536.

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To convert back to floating point, divide this by {{code|1=(2^(wordsize-7-1)) == 21.2800000099}}

Various scalings may be used. B0 for instance can be used to represent any number between -1−1 and 0.999999999.

=={{anchor|BAM}}Binary angles==